No, for one very simple reason: the U.S. Constitution guarantees the right to a free press. The government does not get to shut down a media outlet because they do not like the content of their programming. It doesn't even matter if the media outlet is biased against the President or anyone else. If the government tried to fine or shut down CNN or anybody else, a little institution I like to call the Supreme Court would immediately put an end to the attempt.

There was no fake news. It was just bad reporting and the article was retracted as soon as it was discovered. Fake news is deliberate lying, with no retractions. CNN fires people who do that. Fox News encourages those people.